text_input stringlengths 62 562 | image_input listlengths 1 1 | sequence_plan listlengths 3 14 | original_final_answer stringlengths 0 69 |
|---|---|---|---|
In △ABC, D is the midpoint of BC and E is the midpoint of AD. If BE and CE are connected, and the area of △ABC is 20, then the area of △BCE is (). option:['5', '10', '15', '18'] | [
"images_comt/creation/12035.png"
] | [
{
"type": "text",
"content": "As per the question, the image is represented below:",
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{
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"content": null,
"helper_image": "images_comt/creation/12035.png"
},
{
"type": "text",
"content": "Since D is the midpoint of BC, we have the area ... | 10 |
In △ABC, points D and E are the midpoints of AC and AB, respectively. And the area of △ABC is 12. Connecting BD and DE, the area of △BDE is (). option:['12', '6', '3', '2'] | [
"images_comt/creation/12036.png"
] | [
{
"type": "text",
"content": "Adhering to the provided question, the picture is presented as follows:",
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},
{
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"content": null,
"helper_image": "images_comt/creation/12036.png"
},
{
"type": "text",
"content": "Since point D is the midpoint... | 3 |
AD is the median of △ABC, E is the midpoint of AD, the area of △ABE is 2, the area of △ABC is (). option:['5', '6', '7', '8'] | [
"images_comt/creation/12037.png"
] | [
{
"type": "text",
"content": "Taking into consideration the question, the image is illustrated below:",
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},
{
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"content": null,
"helper_image": "images_comt/creation/12037.png"
},
{
"type": "text",
"content": "Since AD is the median of tri... | 8 |
In Rt△ABC, ∠ACB is equal to 90°. AC is 3 and BC is 4. Use point A as the center, draw an arc with AC as the radius, intersecting AB at point D. The length of BD is (). option:['2', '3', '4', '5'] | [
"images_comt/creation/12044.png"
] | [
{
"type": "text",
"content": "Based on the given question, the picture is illustrated below:",
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},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12044.png"
},
{
"type": "text",
"content": "Since AC = 3 and BC = 4, we have AB = ... | 2 |
In △ABC, AB is perpendicular to BC and AC = 2.5, AB = 1. P is an arbitrary point on BC. The possible length of line segment AP is (). option:['0.5', '0.7', '2.3', '2.8'] | [
"images_comt/creation/12046.png"
] | [
{
"type": "text",
"content": "Adhering to the provided question, the picture is presented as follows:",
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},
{
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"content": null,
"helper_image": "images_comt/creation/12046.png"
},
{
"type": "text",
"content": "∵P is any point on BC, theref... | 2.3 |
In right triangle △ABC, ∠C is equal to 90°. AC is equal to 5 and BC is equal to 12. The measure of AB is (). option:['12', '13', '14', '15'] | [
"images_comt/creation/12050.png"
] | [
{
"type": "text",
"content": "Based on the given question, the picture is illustrated below:",
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},
{
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"content": null,
"helper_image": "images_comt/creation/12050.png"
},
{
"type": "text",
"content": "In Rt△ABC, ∠C = 90°. According to the ... | 13 |
In △ABC, ∠ACB is equal to 90°, AC equals 8, AB equals 10. DE perpendicular bisects AC and intersects AB at point E and intersects AC at point D. The length of DE is (). option:['3', '4', '5', '6'] | [
"images_comt/creation/12051.png"
] | [
{
"type": "text",
"content": "Abiding by the question, the image is depicted below:",
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},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12051.png"
},
{
"type": "text",
"content": "In △ABC, ∠ACB = 90°. By the Pythagorean theorem... | 3 |
In △ABC, ∠ACB is equal to 90°, AC has a length of 6, and BC has a length of 8. The length of the altitude CD on side AB is (). option:['4', '\\frac{24}{5}', '3√{3}', '10'] | [
"images_comt/creation/12053.png"
] | [
{
"type": "text",
"content": "Based on the given question, the picture is illustrated below:",
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},
{
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"content": null,
"helper_image": "images_comt/creation/12053.png"
},
{
"type": "text",
"content": "In triangle ABC, ∠ACB = 90°, AC = 6, B... | \frac{24}{5} |
In △ABC, ∠C = 90°, point D is on side BC, AD = BD, DE bisects ∠ADB and intersects AB at point E. If AC = 12, BC = 16, then the length of AE is () option:['6', '8', '10', '12'] | [
"images_comt/creation/12059.png"
] | [
{
"type": "text",
"content": "Following the given question, here is the image we've created:",
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},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12059.png"
},
{
"type": "text",
"content": "In △ABC, ∠C = 90°, AC = 12, BC = 16. B... | 10 |
Given △ABC, AB = 10, AC = 8, BC = 6, the perpendicular bisector of AC intersects AB at point D, with the foot E, and CD is connected. The length of CD is (). option:['3', '4', '4.8', '5'] | [
"images_comt/creation/12063.png"
] | [
{
"type": "text",
"content": "As per the question, the image is represented below:",
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},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12063.png"
},
{
"type": "text",
"content": "Since AB = 10, AC = 8, BC = 6, we have BC² + AC²... | 5 |
In △ABC, CD is the altitude on side AB. If AB = 1.5, BC = 0.9, and AC = 1.2, then the value of CD is() option:['0.72', '2.0', '1.125', 'uncertain'] | [
"images_comt/creation/12065.png"
] | [
{
"type": "text",
"content": "Adhering to the provided question, the picture is presented as follows:",
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},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12065.png"
},
{
"type": "text",
"content": "Since AB = 1.5, BC = 0.9, AC ... | 0.72 |
OC bisects ∠AOB, point P is a point on OC, and PM is perpendicular to OB at point M. Point N is a moving point on ray OA. If OM=4 and OP=5, the minimum value of PN is () option:['2', '3', '4', '5'] | [
"images_comt/creation/12066.png"
] | [
{
"type": "text",
"content": "Based on the given question, the picture is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12066.png"
},
{
"type": "text",
"content": "Since PM is perpendicular to OB at poi... | 3 |
In △ABC, AD is perpendicular to BC at D, AB = 17, BD = 15, and DC = 6. The length of AC is () option:['11', '10', '9', '8'] | [
"images_comt/creation/12069.png"
] | [
{
"type": "text",
"content": "Following the given question, here is the image we've created:",
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},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12069.png"
},
{
"type": "text",
"content": "Since AD ⊥ BC, we have ∠ADB = ∠ADC = 9... | 10 |
O is the midpoint of the diagonal AC of rectangle ABCD, and M is the midpoint of AD. If AB = 5 and AD = 12, the perimeter of quadrilateral ABOM is (). option:['16', '20', '29', '34'] | [
"images_comt/creation/12070.png"
] | [
{
"type": "text",
"content": "As per the question, the image is represented below:",
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},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12070.png"
},
{
"type": "text",
"content": "∵AB = 5, ∴CD = 5, ∵AD = 12, ∠D = 90°, ∴AC = 13. ... | 20 |
In right triangle △ABC, with ∠BAC equal to 90°, points D, E, and F are respectively the midpoints of the three sides, and DE is equal to 4cm. The length of AF is (). option:['2cm', '3cm', '4cm', '6cm'] | [
"images_comt/creation/12071.png"
] | [
{
"type": "text",
"content": "Following the given question, here is the image we've created:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12071.png"
},
{
"type": "text",
"content": "Since point D and point E are the midp... | 4cm |
Quadrilateral ABCD is a rhombus. Diagonals AC and BD intersect at point O. E is the midpoint of AD. If OE=3.5, then the perimeter of rhombus ABCD is () option:['14', '28', '7', '35'] | [
"images_comt/creation/12072.png"
] | [
{
"type": "text",
"content": "Abiding by the question, the image is depicted below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12072.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a rhombus, we have ... | 28 |
In rhombus ABCD, diagonal AC and BD intersect at point O. Point M is the midpoint of side AB. If MO = 4 cm, then the perimeter of rhombus ABCD is () option:['32cm', '24cm', '16cm', '8cm'] | [
"images_comt/creation/12073.png"
] | [
{
"type": "text",
"content": "According to the given question, the image is depicted as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12073.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a rhom... | 32cm |
In parallelogram ABCD, diagonals AC and BD intersect at point O. OE is parallel to AB and intersects AD at point E. If OA=2 and the perimeter of △AOE is 10, then the perimeter of parallelogram ABCD is (). option:['16', '32', '36', '40'] | [
"images_comt/creation/12074.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12074.png"
},
{
"type": "text",
"content": "Since the quadrilateral ABCD is a paralle... | 32 |
In right triangle △ABC, ∠ACB is equal to 90°. Points H, E, and F are the midpoints of sides AB, BC, and CA, respectively. Connecting EF and CH, if EF + CH = 4, the value of CH is () option:['1.5', '2', '2.5', '3'] | [
"images_comt/creation/12078.png"
] | [
{
"type": "text",
"content": "Adhering to the provided question, the picture is presented as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12078.png"
},
{
"type": "text",
"content": "Since points E and F are the ... | 2 |
The perimeter of ▱ABCD is 36. Diagonals AC and BD intersect at point O. Point E is the midpoint of CD. The perimeter of △DOE is 15. The length of BD is (). option:['18', '16', '14', '12'] | [
"images_comt/creation/12080.png"
] | [
{
"type": "text",
"content": "According to the given question, the image is depicted as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12080.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a para... | 12 |
In equilateral △ABC, points D and E are the midpoints of sides AB and BC, respectively. If DE = 2, then the perimeter of △ABC is () option:['9', '12', '16', '18'] | [
"images_comt/creation/12081.png"
] | [
{
"type": "text",
"content": "In accordance with the provided context, the image is presented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12081.png"
},
{
"type": "text",
"content": "Since D and E are the midpoint... | 12 |
In parallelogram ABCD, the diagonals AC and BD intersect at point O. E is the midpoint of AD. Connect OE. If OE = 3, the length of CD is (). option:['3', '5', '6', '9'] | [
"images_comt/creation/12083.png"
] | [
{
"type": "text",
"content": "Following the question, we present the image as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12083.png"
},
{
"type": "text",
"content": "∵Quadrilateral ABCD is a parallelogram, ther... | 6 |
In rhombus ABCD, AC = 6, BD = 8, AH ⊥ BC at point H, then AH = () option:['24', '10', '\\frac{24}{5}', '\\frac{12}{5}'] | [
"images_comt/creation/12085.png"
] | [
{
"type": "text",
"content": "As per the question, the image is represented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12085.png"
},
{
"type": "text",
"content": "Diagonal AC and BD intersect at point O. Since q... | \frac{24}{5} |
In ▱ABCD, the angle bisector of ∠ABC intersects AD at point E, and the angle bisector of ∠BCD intersects AD at point F. If AB = 4 and AF = 1, then the length of BC is (). option:['4', '5', '7', '6'] | [
"images_comt/creation/12086.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12086.png"
},
{
"type": "text",
"content": "Since the quadrilateral ABCD is a paralle... | 5 |
In △ABC, points D and E are the midpoints of BC and AC, respectively. BF bisects ∠ABC, intersecting DE at point F. If BC = 6, the length of DF is (). option:['2', '3', '6', '4'] | [
"images_comt/creation/12087.png"
] | [
{
"type": "text",
"content": "As per the question, the image is represented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12087.png"
},
{
"type": "text",
"content": "Since D and E are respectively the midpoints of ... | 3 |
In diamond ABCD, AB=5, diagonals AC and BD intersect at point O, and AC=6. AE is perpendicular to CD at point E. The length of AE is () option:['4', '\\frc{12}{5}', '\\frac{24}{5}', '5'] | [
"images_comt/creation/12088.png"
] | [
{
"type": "text",
"content": "Following the question, we present the image as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12088.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a diamond, we ha... | \frac{24}{5} |
In quadrilateral ABCD, AD is parallel to BC, AD = 2, BC = 5. Connect AC, BD, points E and F are the midpoints of diagonals AC and BD respectively. Connect EF, then the length of EF is () option:['1', '1.5', '2.5', '3.5'] | [
"images_comt/creation/12089.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12089.png"
},
{
"type": "text",
"content": "Since the midpoint of DC is G, connect FG... | 1.5 |
In ▱ABCD, BC is equal to 10, AC is equal to 8, and BD is equal to 14. Points AC and BD intersect at point O. The perimeter of △AOD is (). option:['16', '20', '21', '23'] | [
"images_comt/creation/12092.png"
] | [
{
"type": "text",
"content": "According to the given question, the image is depicted as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12092.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a para... | 21 |
Given △ABC, points D, E, F are the midpoints of sides BC, CA, AB, respectively. AB = 10, AC = 8. Connect DE, EF, FD. The perimeter of quadrilateral AFDE is equal to () option:['18', '16', '14', '12'] | [
"images_comt/creation/12093.png"
] | [
{
"type": "text",
"content": "Adhering to the provided question, the picture is presented as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12093.png"
},
{
"type": "text",
"content": "Since D, E, and F are the mid... | 18 |
In the parallelogram ABCD, diagonals AC and BD intersect at point O. If AC = 12, BD = 16, and CD = 11, the perimeter of △DOC is (). option:['39', '31', '33', '25'] | [
"images_comt/creation/12094.png"
] | [
{
"type": "text",
"content": "Following the question, we present the image as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12094.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a parallelogram ... | 25 |
In ▱ABCD, E is the midpoint of BC. DE is perpendicular to AE. F is the midpoint of AD. Connect EF. AE = 6, DE = 8. The length of AB is () option:['3', '4', '5', '6'] | [
"images_comt/creation/12095.png"
] | [
{
"type": "text",
"content": "Taking into consideration the question, the image is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12095.png"
},
{
"type": "text",
"content": "Since DE is perpendicular to ... | 5 |
Quadrilateral ABCD is a rhombus, the coordinates of points A and B are (√3, 0) and (0, 1) respectively. Points C and D lie on the coordinate axes. Therefore, the perimeter of rhombus ABCD is () option:['8', '4', '6', '5'] | [
"images_comt/creation/12096.png"
] | [
{
"type": "text",
"content": "Following the given question, here is the image we've created:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12096.png"
},
{
"type": "text",
"content": "Since the coordinates of points A and ... | 8 |
In parallelogram ABCD, AD is equal to 8 and AB is equal to 3. AE bisects ∠BAD and intersects BC at point E. The length of CE is () option:['2', '3', '4', '5'] | [
"images_comt/creation/12097.png"
] | [
{
"type": "text",
"content": "Following the given question, here is the image we've created:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12097.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a parallel... | 5 |
In rectangle ABCD, AB = 12. Point E is a point on AD, and AE = 6. The perpendicular bisector of BE intersects the extension of BC at point F. Connecting EF intersects CD at point G. If G is the midpoint of CD, the length of BC is () option:['12.5', '12', '10', '10.5'] | [
"images_comt/creation/12098.png"
] | [
{
"type": "text",
"content": "Taking into consideration the question, the image is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12098.png"
},
{
"type": "text",
"content": "Since G is the midpoint of CD... | 10.5 |
Quadrilateral ABCD is a rhombus. AC is equal to 8cm, DB is equal to 6cm. DH is perpendicular to AB at H. Therefore, DH is equal to (). option:['3.6', '4.8', '5', '10'] | [
"images_comt/creation/12099.png"
] | [
{
"type": "text",
"content": "As per the question, the image is represented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12099.png"
},
{
"type": "text",
"content": "Assuming AC and BD intersect at point O, since t... | 4.8 |
In quadrilateral ▱ABCD, diagonals AC and BD intersect at point O, and AC equals 4. Points E, F, and G are the midpoints of AO, OB, and OC, respectively. Connect EF and FG. If the perimeter of △EFG is 7, then the perimeter of ▱ABCD is (). option:['10', '15', '20', '25'] | [
"images_comt/creation/12100.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12100.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a parallelogr... | 20 |
In the parallelogram ABCD, AC intersects BD at point O. ∠BAC is equal to 90°. Point E is the midpoint of BC and AE is equal to 3.5cm. The perimeter of triangle AOD is 3cm greater than the perimeter of triangle AOB. Therefore, the perimeter of parallelogram ABCD is () option:['20cm', '21cm', '22cm', '23cm'] | [
"images_comt/creation/12101.png"
] | [
{
"type": "text",
"content": "Following the question, we present the image as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12101.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a parallelogram,... | 22cm |
Triangle ABC has a perimeter of 4, where points D, E, F are the midpoints of AB, BC, and CA, respectively. The perimeter of triangle DEF is () option:['1', '2', '3', '4'] | [
"images_comt/creation/12102.png"
] | [
{
"type": "text",
"content": "Based on the given question, the picture is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12102.png"
},
{
"type": "text",
"content": "Since the perimeter of triangle ABC is... | 2 |
In Rt△ABC, ∠ACB is equal to 90°. D, E, and F are the midpoints of sides AB, AC, and BC, respectively. Connect EF and CD. If EF is equal to 5 and BC is equal to 4, the length of CD is (). option:['5', '6', '8', '10'] | [
"images_comt/creation/12103.png"
] | [
{
"type": "text",
"content": "In accordance with the provided context, the image is presented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12103.png"
},
{
"type": "text",
"content": "Since triangle ABC is a right ... | 5 |
In ▱ABCD, point F on BC bisects ∠BAD while point E on AD bisects ∠ABC. Connecting EF, if AF = 6 and BE = 8, then the length of AB is (). option:['6', '5', '4', '3'] | [
"images_comt/creation/12104.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12104.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a parallelogr... | 5 |
In ▱ABCD, diagonal lines AC and BD intersect at point O. Point E is the midpoint of BC. Connecting OE, if OE=8, then the length of AB is () option:['16', '18', '20', '22'] | [
"images_comt/creation/12105.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12105.png"
},
{
"type": "text",
"content": "∵ The quadrilateral ABCD is a parallelogr... | 16 |
In quadrilateral ABCD, diagonal AC intersects BD at point O. Point E is the midpoint of BC. If the perimeter of quadrilateral ABCD is 10 and OE is 1, the length of BC is (). option:['4', '3', '2', '1'] | [
"images_comt/creation/12106.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12106.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a parallelogr... | 3 |
AD is the angle bisector of △ABC, and point E is the midpoint of AC. Connect DE. If AB=AC=10 and BC=8, then the perimeter of △CDE is (). option:['20', '12', '13', '14'] | [
"images_comt/creation/12107.png"
] | [
{
"type": "text",
"content": "Adhering to the provided question, the picture is presented as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12107.png"
},
{
"type": "text",
"content": "Since AB = AC and AD is the a... | 14 |
In △ABC, D and E are the midpoints of AB and AC, respectively. F is a point on DE. AF and CF are connected and ∠AFC is equal to 90°. If DF is equal to 1 and AC is equal to 6, then the length of BC is (). option:['5', '6', '7', '8'] | [
"images_comt/creation/12108.png"
] | [
{
"type": "text",
"content": "Following the question, we present the image as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12108.png"
},
{
"type": "text",
"content": "In right triangle AFC, point E is the midpoi... | 8 |
In ▱ABCD, connect AC. If ∠ABC = ∠CAD = 60° and AB = 3, then the length of AD is (). option:['3', '6', '9', '18'] | [
"images_comt/creation/12109.png"
] | [
{
"type": "text",
"content": "Based on the given question, the picture is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12109.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a parallel... | 3 |
In quadrilateral ABCD, the perimeter is 36. Diagonals AC and BD intersect at point O. Point E is the midpoint of CD and BD = 12. Connect OE. The perimeter of triangle DOE is (). option:['15', '18', '21', '24'] | [
"images_comt/creation/12110.png"
] | [
{
"type": "text",
"content": "According to the given question, the image is depicted as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12110.png"
},
{
"type": "text",
"content": "Since the perimeter of parallelogr... | 15 |
In figure ▱ABCD, the diagonals AC and BD intersect at point O, and AC+BD=16. If the perimeter of △BCO is 14, then the length of BC is (). option:['12', '9', '8', '6'] | [
"images_comt/creation/12111.png"
] | [
{
"type": "text",
"content": "Following the given question, here is the image we've created:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12111.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a parallel... | 6 |
In rectangle ABCD, point O is the midpoint of diagonal AC, and point M is the midpoint of AD. If AB = 5 and AD = 12, the length of OM + OB is (). option:['7', '8', '9', '10'] | [
"images_comt/creation/12112.png"
] | [
{
"type": "text",
"content": "As per the question, the image is represented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12112.png"
},
{
"type": "text",
"content": "- Thus, since the quadrilateral ABCD is a rectan... | 9 |
In △ABC, points D and E are respectively the midpoints of the sides AB and BC. Connecting DE, if the perimeter of △BDE is 6, then the perimeter of △ABC is () option:['8', '10', '12', '14'] | [
"images_comt/creation/12114.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12114.png"
},
{
"type": "text",
"content": "Since the perimeter of triangle BDE is 6,... | 12 |
In rectangle ABCD, the two diagonals intersect at point O. ∠AOB is equal to 60° and AC is equal to 8. The length of side AB is (). option:['4', '5', '6', '8'] | [
"images_comt/creation/12116.png"
] | [
{
"type": "text",
"content": "Taking into consideration the question, the image is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12116.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a... | 4 |
In triangle △ABC, points D and E are the midpoints of sides AB and AC, respectively. If DE = 4, then BC equals () option:['2', '4', '8', '10'] | [
"images_comt/creation/12117.png"
] | [
{
"type": "text",
"content": "Following the question, we present the image as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12117.png"
},
{
"type": "text",
"content": "Since D and E are the midpoints of AB and AC... | 8 |
In △ABC, points D, E, and F are the midpoints of the three sides. AB = 6, AC = 4. Connect DE and DF, then the perimeter of quadrilateral AEDF is () option:['40', '30', '20', '10'] | [
"images_comt/creation/12118.png"
] | [
{
"type": "text",
"content": "Adhering to the provided question, the picture is presented as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12118.png"
},
{
"type": "text",
"content": "Since in △ABC, E, D, and F ar... | 10 |
In rhombus ABCD with a side length of 10, E is the midpoint of AD, and O is the intersection of the diagonals. One side FG of rectangle OEFG lies on AB, and EF = 4. The length of BG is () option:['3', '2', '√{2}', '1'] | [
"images_comt/creation/12119.png"
] | [
{
"type": "text",
"content": "In accordance with the provided context, the image is presented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12119.png"
},
{
"type": "text",
"content": "Since the quadrilateral ABCD i... | 2 |
In ▱ABCD, AD = 7, AB = 5, DE bisects ∠ADC and intersects BC at point E. The length of BE is () option:['2', '3', '4', '5'] | [
"images_comt/creation/12120.png"
] | [
{
"type": "text",
"content": "Following the question, we present the image as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12120.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a parallelogram,... | 2 |
In rectangle ABCD, the diagonals AC and BD intersect at point O. Points E and F are the midpoints of AB and AO, respectively, and AC = 8. Connect EF, then the length of EF is (). option:['2', '4', '6', '8'] | [
"images_comt/creation/12121.png"
] | [
{
"type": "text",
"content": "As per the question, the image is represented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12121.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a rectangle, we have... | 2 |
In ∆ABC, points D, E, and F are the midpoints of sides AB, BC, and CA, respectively, and AB = 8cm, AC = 10cm. If we connect DE and EF, then the perimeter of quadrilateral ADEF is equal to () option:['14', '18', '20', '24'] | [
"images_comt/creation/12122.png"
] | [
{
"type": "text",
"content": "According to the given question, the image is depicted as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12122.png"
},
{
"type": "text",
"content": "Since points D, E, and F are the m... | 18 |
The perimeter of ▱ABCD is 40, AD:AB=3:2, then the length of BC is () option:['8', '12', '16', '24'] | [
"images_comt/creation/12123.png"
] | [
{
"type": "text",
"content": "In accordance with the provided context, the image is presented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12123.png"
},
{
"type": "text",
"content": "Since the perimeter of square ... | 12 |
In ▱ABCD, if the perimeter of △ACD is 13cm and AC = 4cm, the perimeter of ▱ABCD is () option:['17', '', '18', '', '22', '', '34', ''] | [
"images_comt/creation/12125.png"
] | [
{
"type": "text",
"content": "Taking into consideration the question, the image is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12125.png"
},
{
"type": "text",
"content": "Since AC = 4cm, the perimeter... | |
In rhombus ABCD, diagonal AC intersects diagonal BD at point O. Point H is the midpoint of side AD. The perimeter of the rhombus is 28. If OH is connected, then the length of OH is (). option:['3.5', '4.5', '7', '14'] | [
"images_comt/creation/12126.png"
] | [
{
"type": "text",
"content": "Taking into consideration the question, the image is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12126.png"
},
{
"type": "text",
"content": "Since the perimeter of rhombu... | 3.5 |
In ▱ABCD, AC = 5cm. If the perimeter of △ACD is 14cm, then the perimeter of ▱ABCD is () option:['18cm', '19cm', '28cm', '38cm'] | [
"images_comt/creation/12127.png"
] | [
{
"type": "text",
"content": "According to the given question, the image is depicted as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12127.png"
},
{
"type": "text",
"content": "- ∵ The perimeter of △ACD is 14cm,... | 18cm |
Given that diamond ABCD, connecting AC and BD, BD = 8 and the area is 24, the perimeter of diamond ABCD is () option:['5', '10', '10√{2}', '20'] | [
"images_comt/creation/12128.png"
] | [
{
"type": "text",
"content": "According to the given question, the image is depicted as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12128.png"
},
{
"type": "text",
"content": "Assume AC intersects BD at point O... | 20 |
In △ABC, AB is equal to 7, AC is equal to 6, and BC is equal to 5. D and E are the midpoints of AB and AC, respectively. Connect DE. The length of DE is (). option:['4', '3.5', '3', '2.5'] | [
"images_comt/creation/12129.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12129.png"
},
{
"type": "text",
"content": "Since D and E are the midpoints of AB and... | 2.5 |
In rhombus ABCD, diagonal AC intersects BD at point O, while E is the midpoint of DC. If the perimeter of the rhombus is 16 and the length of OE is (), then the answer is (). option:['2', '1', '4', '3'] | [
"images_comt/creation/12130.png"
] | [
{
"type": "text",
"content": "Abiding by the question, the image is depicted below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12130.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a rhombus, we have ... | 2 |
In ▱ABCD, diagonal AC intersects diagonal BD at point O. If AD = 5, AC = 10, and BD = 6, the perimeter of △BOC is (). option:['13', '16', '18', '21'] | [
"images_comt/creation/12131.png"
] | [
{
"type": "text",
"content": "Following the question, we present the image as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12131.png"
},
{
"type": "text",
"content": "Since the two diagonals of square ABCD inter... | 13 |
In △ABC, point M is the midpoint of BC. AD bisects ∠BAC, BD is perpendicular to AD at point D, and extended to intersect AC at point N. If AB = 10 and AC = 16, then the length of MD is (). option:['3', '4', '6', '7.5'] | [
"images_comt/creation/12132.png"
] | [
{
"type": "text",
"content": "Adhering to the provided question, the picture is presented as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12132.png"
},
{
"type": "text",
"content": "Since AD bisects ∠BAC, we hav... | 3 |
In △ABC, D, E and F are the midpoints of BC, AC and AB, respectively. Point H is the foot of the altitude from A to BC. Connecting FD, EF and HE, if FD = 8, then HE is equal to () option:['4', '6', '8', '10'] | [
"images_comt/creation/12133.png"
] | [
{
"type": "text",
"content": "Following the given question, here is the image we've created:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12133.png"
},
{
"type": "text",
"content": "∵D and F are respectively the midpoint... | 8 |
In rectangle ABCD, diagonal AC intersects diagonal BD at point O. DE is perpendicular to AC, and its foot is E. If AO:OE is 3:2 and DE is equal to 2√{5}, then the length of CE is (). option:['1', '2', '√{5}', '√{2}'] | [
"images_comt/creation/12134.png"
] | [
{
"type": "text",
"content": "According to the given question, the image is depicted as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12134.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a rect... | 2 |
In ▱ABCD, BE bisects ∠ABC and intersects AD at point E. AE is equal to 2 and ED is equal to 1. The perimeter of ▱ABCD is (). option:['14', '12', '10', '8'] | [
"images_comt/creation/12135.png"
] | [
{
"type": "text",
"content": "Based on the given question, the picture is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12135.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a parallel... | 10 |
In ▱ABCD, AE bisects ∠DAB and intersects CD at point E. If AB = 6 and CE = 2, the perimeter of ▱ABCD is (). option:['14', '16', '20', '24'] | [
"images_comt/creation/12136.png"
] | [
{
"type": "text",
"content": "Adhering to the provided question, the picture is presented as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12136.png"
},
{
"type": "text",
"content": "Since AE bisects ∠BAD, we hav... | 20 |
The diagonal AC of quadrilateral ABCD intersects BD at point O. Point E is the midpoint of AB. Connecting OE, the perimeter of triangle BEO is 20, then the perimeter of triangle BCD is () option:['30', '40', '50', '60'] | [
"images_comt/creation/12137.png"
] | [
{
"type": "text",
"content": "Taking into consideration the question, the image is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12137.png"
},
{
"type": "text",
"content": "Since the diagonals AC and BD... | 40 |
In quadrilateral ABCD, CE bisects angle DCB, intersects AB at point E, AE=2, DC=6, the perimeter of quadrilateral ABCD is () option:['16', '18', '20', '24'] | [
"images_comt/creation/12138.png"
] | [
{
"type": "text",
"content": "As per the question, the image is represented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12138.png"
},
{
"type": "text",
"content": "In quadrilateral ABCD, CE bisects ∠BCD, so ∠DCE ... | 20 |
In right triangle △ABC, ∠ACB=90°, points G, E, D are the midpoints of sides AB, BC, CA, respectively. Connecting DE, CG, if DE+CG=7, then the length of CG is () option:['3', '3.5', '4', '5'] | [
"images_comt/creation/12139.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12139.png"
},
{
"type": "text",
"content": "In right triangle ABC, ∠ACB = 90°. Point ... | 3.5 |
In ▱ABCD, AE is perpendicular to BC at point E, and AF is perpendicular to CD at point F, with AE = 3 and AF = 4. If the perimeter of ▱ABCD is 56, then the length of BC is () option:['14', '16', '28', '32'] | [
"images_comt/creation/12140.png"
] | [
{
"type": "text",
"content": "As per the question, the image is represented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12140.png"
},
{
"type": "text",
"content": "Since the perimeter of square ABCD is 56, we hav... | 16 |
AC is the diagonal of rectangle ABCD. The bisector of ∠BAC intersects BC at point E. BM is perpendicular to AE at point M, and intersects AC at point F. If N is the midpoint of BC, connect MN. Given AB = 6 and BC = 8, the length of MN is (). option:['3.5', '3', '2.5', '2'] | [
"images_comt/creation/12141.png"
] | [
{
"type": "text",
"content": "According to the given question, the image is depicted as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12141.png"
},
{
"type": "text",
"content": "∵Quadrilateral ABCD is a rectangle... | 2 |
The perimeter of rhombus ABCD is 16. Connecting AC and BD, ∠DAB = 60°, then the length of BD is () option:['10', '8', '4', '2'] | [
"images_comt/creation/12142.png"
] | [
{
"type": "text",
"content": "Taking into consideration the question, the image is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12142.png"
},
{
"type": "text",
"content": "Since the perimeter of rhombu... | 4 |
In the right triangle △ABC as shown in the figure, ∠C is equal to 90° and AB is equal to 10cm. Point D is the midpoint of AB. The length of CD is (). option:['7cm', '6cm', '5cm', '4cm'] | [
"images_comt/creation/12144.png"
] | [
{
"type": "text",
"content": "In accordance with the provided context, the image is presented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12144.png"
},
{
"type": "text",
"content": "Since ∠C = 90°, AB = 10cm, and... | 5cm |
The diagonal AC of the parallelogram intersects with the diagonal BD at point O. Given that BC = 6, BD = 12, and AC = 8, then the perimeter of triangle OAD is () option:['13', '14', '16', '18'] | [
"images_comt/creation/12145.png"
] | [
{
"type": "text",
"content": "According to the given question, the image is depicted as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12145.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a para... | 16 |
In right triangle △ABC, ∠ACB is equal to 90°. Points D and E are the midpoints of sides AB and AC, respectively. BC is extended to point F such that CF is equal to half of BC. CD, DE, and EF are connected. If EF is equal to 5, then the length of side AB is () option:['10', '12', '15', '18'] | [
"images_comt/creation/12146.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12146.png"
},
{
"type": "text",
"content": "Since points D and E are the midpoints of... | 10 |
Rectangle ABCD's diagonal AC is equal to 8. AC intersects BD at point O. ∠BOC is equal to 120°. The length of AB is () option:['3', '4', '5', '6'] | [
"images_comt/creation/12148.png"
] | [
{
"type": "text",
"content": "As per the question, the image is represented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12148.png"
},
{
"type": "text",
"content": "∵Quadrilateral ABCD is a rectangle, therefore AC... | 4 |
In △ABC, points D and E are the midpoints of AB and AC, respectively. Point F is on DE, and AF is perpendicular to CF. If AC = 3 and BC = 6, then the length of DF is () option:['1.5', '1', '0.5', '2'] | [
"images_comt/creation/12149.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12149.png"
},
{
"type": "text",
"content": "Since D and E are the midpoints of AB and... | 1.5 |
In ▱ABCD, DE bisects ∠ADC, intersecting BC at point E, AD = 9, BE = 3, then the perimeter of ▱ABCD is () option:['15', '24', '30', '36'] | [
"images_comt/creation/12151.png"
] | [
{
"type": "text",
"content": "Based on the given question, the picture is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12151.png"
},
{
"type": "text",
"content": "In quadrilateral ABCD, AD = 9, so BC =... | 30 |
In rhombus ABCD, points A, C, and B, D are connected at point O. AB is equal to 13 and AC is equal to 10. The length of BD is () option:['24', '16', '12', '8'] | [
"images_comt/creation/12152.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12152.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a rhombus, we... | 24 |
In parallelogram ABCD, diagonals AC and BD intersect at point O. E is the midpoint of AB. Connect OE. If AE + EO = 4, then the perimeter of parallelogram ABCD is (). option:['16', '20', '12', '8'] | [
"images_comt/creation/12153.png"
] | [
{
"type": "text",
"content": "Taking into consideration the question, the image is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12153.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a... | 16 |
In Rt△ABC, D is the midpoint of AB, AB = 10, then CD is () option:['3', '4', '5', '6'] | [
"images_comt/creation/12154.png"
] | [
{
"type": "text",
"content": "According to the given question, the image is depicted as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12154.png"
},
{
"type": "text",
"content": "Since ∠ACB = 90° and D is the midp... | 5 |
In Rt△ABC, ∠C is equal to 90°. AB is equal to 10cm and AC is equal to 8cm. Point D is a point on AC. Using AD and BD as adjacent sides, we construct a parallelogram ADBE. The minimum value of the diagonal DE is (). option:['4', '6', '8', '10'] | [
"images_comt/creation/12155.png"
] | [
{
"type": "text",
"content": "In accordance with the provided context, the image is presented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12155.png"
},
{
"type": "text",
"content": "-AB intersects DE at point O, ... | 6 |
In rhombus ABCD, points E and F are the midpoints of AD and AC, respectively. If EF = 3, what is the perimeter of rhombus ABCD? () option:['6', '18', '24', '30'] | [
"images_comt/creation/12156.png"
] | [
{
"type": "text",
"content": "Abiding by the question, the image is depicted below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12156.png"
},
{
"type": "text",
"content": "Since E and F are the midpoints of AD and AC re... | 24 |
In ▱ABCD, points A, C, and BD intersect at point O. Point E is the midpoint of AD, and OE is connected. If OE = 2, the length of CD is (). option:['1', '2', '3', '4'] | [
"images_comt/creation/12157.png"
] | [
{
"type": "text",
"content": "Adhering to the provided question, the picture is presented as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12157.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a... | 4 |
In quadrilateral ABCD, the angle bisector of ∠BCD intersects the extension of BA at point E, and AE = 2, AD = 5. The length of CD is (). option:['4', '3', '2', '1.5'] | [
"images_comt/creation/12158.png"
] | [
{
"type": "text",
"content": "In accordance with the provided context, the image is presented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12158.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a ... | 3 |
In rhombus ABCD, diagonals AC and BD intersect at point O. E is the midpoint of CD. Connecting OE, if OE = 3, then the length of AB is () option:['6', '5', '4', '3'] | [
"images_comt/creation/12159.png"
] | [
{
"type": "text",
"content": "As per the question, the image is represented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12159.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a rhombus, we have A... | 6 |
In parallelogram ABCD, diagonal AC intersects at point O, and AD > CD. Perpendicular line OM is drawn from point O to AC, intersecting AD at point M. If the perimeter of △CDM is 7.5, then the perimeter of parallelogram ABCD is (). option:['7.5', '15', '17', '19'] | [
"images_comt/creation/12160.png"
] | [
{
"type": "text",
"content": "As per the question, the image is represented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12160.png"
},
{
"type": "text",
"content": "∵ Quadrilateral ABCD is a parallelogram, ∴ AO = ... | 15 |
In △ABC, AB=AC=10, BC=8, AD is perpendicular to BC at point D. Point E is the midpoint of AC. Connect DE. The length of DE is (). option:['4', '5', '6', '8'] | [
"images_comt/creation/12161.png"
] | [
{
"type": "text",
"content": "According to the given question, the image is depicted as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12161.png"
},
{
"type": "text",
"content": "Since AB = AC, AD ⊥ BC, therefore ... | 5 |
In parallelogram ABCD, diagonals AC and BD intersect at point O. E is the midpoint of side BC. AB = 4. If OE is connected, then OE = () option:['1', '2', '4', '8'] | [
"images_comt/creation/12162.png"
] | [
{
"type": "text",
"content": "Based on the given question, the picture is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12162.png"
},
{
"type": "text",
"content": "∵The quadrilateral ABCD is a parallelo... | 2 |
In △ABC, AB = 8, BC = 12, points D and E are the midpoints of sides AB and AC, respectively. Point F is a point on segment DE. Connect AF and BF, if ∠AFB = 90°, the length of segment EF is () option:['4', '3', '2', '1'] | [
"images_comt/creation/12163.png"
] | [
{
"type": "text",
"content": "Based on the given question, the picture is illustrated below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12163.png"
},
{
"type": "text",
"content": "Since points D and E are the midpoints... | 2 |
The distance from the midpoint M of the side of rhombus ABCD to the intersection point O of the diagonals is 3cm, then the perimeter of rhombus ABCD is () option:['10cm', '12cm', '16', '', '24', ''] | [
"images_comt/creation/12164.png"
] | [
{
"type": "text",
"content": "As dictated by the question, the image is shown as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12164.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a rhombus, we... | |
In △ABC, points D and E are the midpoints of AB and AC, respectively. Point F is a point on DE, connecting AF and CF, with ∠AFC = 90°. If BC = 12 and AC = 8, then the length of DF is () option:['1', '2', '3', '4'] | [
"images_comt/creation/12165.png"
] | [
{
"type": "text",
"content": "In accordance with the provided context, the image is presented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12165.png"
},
{
"type": "text",
"content": "Since point D and point E are ... | 2 |
In the diamond ABCD, diagonals AC and BD intersect at point O. Point M is the midpoint of DC. If the perimeter of the diamond ABCD is 24, when connecting OM, the length of OM is (). option:['12', '8', '6', '3'] | [
"images_comt/creation/12166.png"
] | [
{
"type": "text",
"content": "According to the given question, the image is depicted as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12166.png"
},
{
"type": "text",
"content": "Since the perimeter of rhombus ABC... | 3 |
In ▱ABCD, BD is perpendicular to AD. AB = 10 and AD = 6. A rectangle DEBF is constructed, where E and F are located on AB and CD, respectively. The length of the diagonal EF is (). option:['8', '9', '10', '11'] | [
"images_comt/creation/12167.png"
] | [
{
"type": "text",
"content": "In accordance with the provided context, the image is presented below:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12167.png"
},
{
"type": "text",
"content": "∵Since BD is perpendicular to ... | 8 |
In quadrilateral ABCD, points AC and BD intersect at point O. Given that ∠ADB = 90°, AC = 10, and AD = 4. The length of BD is () option:['4', '5', '6', '7'] | [
"images_comt/creation/12168.png"
] | [
{
"type": "text",
"content": "Adhering to the provided question, the picture is presented as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12168.png"
},
{
"type": "text",
"content": "Since quadrilateral ABCD is a... | 6 |
In right triangle △ABC, ∠ACB = 90°. D is the midpoint of side AB, AB = 6. If CD is connected, then the length of CD is () option:['2', '3', '4', '6'] | [
"images_comt/creation/12169.png"
] | [
{
"type": "text",
"content": "Adhering to the provided question, the picture is presented as follows:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12169.png"
},
{
"type": "text",
"content": "In Rt△ABC, since ∠ACB = 90° a... | 3 |
In △ABC, points D and E are the midpoints of BC and BA, respectively. If AC=4, then DE=() option:['1', '2', '4', '8'] | [
"images_comt/creation/12170.png"
] | [
{
"type": "text",
"content": "Following the given question, here is the image we've created:",
"helper_image": null
},
{
"type": "latent",
"content": null,
"helper_image": "images_comt/creation/12170.png"
},
{
"type": "text",
"content": "Since point D and point E are respecti... | 2 |
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